Semi‐topological properties

Abstract

ABSTRACT. A property preserved under a semi-homeomorphism is said to be a seml-topologJcal property. In the present paper we prove the following results:{I} A topological property P is semi-topological if and only if the statement '(X.?) has P if and only if (X.F(f)) has P' is true where F() is the finest topology on X having the same family of semi-open sets as (X.T), (2) If P is a topological property being minimal P is semi-topologlcal if and only if for each minimal P space {X,T}, T F{T).

Relative Separation Axioms via Semi-Open Sets

“…Hamlett showed that the property of a topological space being a Baire space is semi-topological [11]. Nayar and Arya [18] developed techniques which help to establish whether a topological property is semi-topological or not. Till now a lot of work has been done in general topology using semi-open sets.…”